Nonlinear Filtering of Chaos for Real Time Applications

Kontorovich, Valeri; Lovtchikova, Z.

doi:10.1007/978-3-642-37781-5_3

Cited by 9 publications

(49 citation statements)

References 14 publications

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“…The reason behind this is the identification of Eq. (1) is an identification of the "inertial vector nonlinear system" which does not have an unique solution and can be formulated only for a previously defined class of nonlinear systems; the complexity of this task has been addressed elsewhere [8,9,18,20] and will not be considered in the following. As examples for F(•), which will be used in the following, there are the equations for the chaotic attractors corresponding to Rossler, Lorenz, and Chua types [8,9]…”

Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

“…The solutions proposed hereafter might be encountered from the structural analysis of the quasi-optimum filtering algorithms for weak chaos in presence of AWGN [8,9] and are synthesized in the following for convenience.…”

Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

“…When one uses the SDE Eq. (5) as a model for chaos, the first strategy that comes up immediately to mind is the nonlinear filtering of chaotic signals which was rigorously developed in [8,9]. The kernel presented in [8] is the Stratonovich-Kushner equation (SKE) [4,5], which allows to describe the dynamic equation for the a posteriori probability density function for the chaos x(t).…”

Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

“…The dynamic filtering approach, such as classic linear Kalman filtering, has been applied for many problems long ago [6] and recently as well [7]. However, in the following the dynamic filtering is proposed adopting a different (nonlinear) angle [8,9], namely, using signals from nonlinear chaotic attractors as a model for the desired signals arriving at the filtering structure. The modeling of real phenomena using chaos has been used for more than 50 years, and there is a wide range of scientific and practical applications, such as seismology [10][11][12], statistical theory of communication [13,14], control, geophysics, biomedical telemetry [15,16] under water signal processing [17], and many other areas related to applied physics as well [18].…”

Section: Introductionmentioning

confidence: 99%

“…Chaos modeling might be immensely useful because almost all quasi-optimum filtering algorithms (which formally are nonlinear but are essentially quasi-linear) show rather high precision in the sense of low NMSE (≤1%) and exhibit low computational complexity among other benefits. These properties were broadly discussed in [8,9], where theoretical proofs can be found. The material presented here contains some experimental applications, for rather different scenarios that apply and extend the ideas presented in [9], and so, both have to be considered together.…”

Section: Introductionmentioning

confidence: 99%

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Ubiquitous Filtering for Nonlinear Problems

Kontorovich¹,

Ramos-Alarcon²

2020

Research Advances in Chaos Theory

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This chapter develops and extends the general theoretical results, previously published in the chapter "Nonlinear filtering of weak chaotic signals", and presents detailed implementations of a computationally simple, robust (filtering fidelity almost insensitive to changes of the desired input signal properties) and rather precise approach for the filtering of weak signals of different physical nature (biological, seismic, voice, etc.) in presence of white Gaussian noise. The implementations rely on non-linear filtering techniques that in general can be considered as either one-moment or multi-moment, in the sense that they operate with a single sample (instantaneous fashion) or with various adjacent samples (non-instantaneous fashion). Chaotic modeling of the real input signals allows achieving an almost ubiquitous filtering approach with a computationally simple implementation. Application of the linearization strategies (for both one and twomoment filtering) provide, additionally, "invariance" of the processing algorithms to variations on the nature and statistics of the input signals.

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Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

Section: Extraction Of Some Theoretical Principles 21 Chaotic Modelimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ubiquitous Filtering for Nonlinear Problems

Kontorovich¹,

Ramos-Alarcon²

2020

Research Advances in Chaos Theory

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Comments on SIC Design for SISO NOMA Systems Over Doubly Selective Channels

Kontorovitch

2022

IEEE Open J. Veh. Technol.

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Non-orthogonal multiple access principle applied in power domain (power-domain NOMA) enhances spectrum efficiency and connectivity of mobile communication systems through sharing between Orthogonal Multiple Access (OMA) and other multiple users. It is the almost main current trend for research and standards for 5G and beyond. Spectrum sharing generates multi-users interference (Multiple Access Interference, MAI) which destroys orthogonality in OMA systems. Meanwhile the so-called Successive Interference Cancellation (SIC) techniques are used to suppress MAI and the Cognitive Radio (CR) principle (CR-NOMA) for decoding order for multiple users inspired effective SIC algorithms. The CR-NOMA principle is applied in the present material as well, but with significant changes for SIC design as for Doubly Selective channels. Due to the above reasons, two original SIC design methods are proposed hereafter following the CR-NOMA principle. Regarding to it the OMA signal (primary user) is decoded first using a Chaos-based quasi-optimum Extended Kalman Filter (EKF). The set of "secondary users" (multiusers) are proposed to be decoded secondly by the following two different methods: Chaos-based EKF filters or, sequential m hypothesis testing. The proposed approach for SIC design is rather simple, fast and accurate for practical implementation.

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Filtraje robusto de señales débiles de fenómenos reales

Kontorovich

Ramos-Alarcon

2019

ings

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En un gran número de escenarios de la vida real se requiere procesar señales de interés que se encuentran muy inmersas en medio de ruido de fondo: señales tectónicas de las entrañas de la Tierra, otras provenientes del lejano cosmos, de telemetría biomédica, acústicas lejanas, interfaces neuronales no invasivas, etc. El propósito de este trabajo es presentar la descripción de una plataforma robusta y eficiente para hacer filtraje en tiempo real de señales muy inmersas en ruido (bastante débiles) y de naturaleza muy diferente. La estrategia propuesta se basa en dos principios: el modelado de las señales de los fenómenos físicos mediante procesos caóticos y la aplicación de estrategias de filtraje basadas en la teoría de sistemas dinámicos no lineales. Tomando como caso de estudio señales sísmicas, señales de electrocardiogramas fetales, señales de tipo voz y señales de interferencias de radiofrecuencia, este trabajo experimental muestra que la metodología es eficiente (error cuadrático medio menor al 1 %) y robusta (la estructura de filtraje, basada en filtro de Kalman, es invariante ante diferentes señales fenomenológicas). La metodología presentada resulta ser muy atractiva para aplicaciones prácticas para la detección de señales débiles en tiempo real por su alta precisión de filtraje con una mínima complejidad computacional y tiempos de procesamiento muy cortos.

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Nonlinear Filtering of Chaos for Real Time Applications

Cited by 9 publications

References 14 publications

Ubiquitous Filtering for Nonlinear Problems

Ubiquitous Filtering for Nonlinear Problems

Comments on SIC Design for SISO NOMA Systems Over Doubly Selective Channels

Filtraje robusto de señales débiles de fenómenos reales

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